arXiv:2510.08661v1 Announce Type: cross Abstract: Recent research demonstrates that linear models achieve forecasting performance competitive with complex architectures, yet methodologies for enhancing linear models remain underexplored. Motivated by the hypothesis that distinct time series instances may follow heterogeneous linear mappings, we propose the Classification Auxiliary Trend-Seasonal Decoupling Linear Model CATS-Linear, employing Classification Auxiliary Channel-Independence (CACI). CACI dynamically routes instances to dedicated predictors via classification, enabling supervised channel design. We further analyze the theoretical expected risks of different channel settings. Additionally, we redesign the trend-seasonal decomposition architecture by adding a decoupling -- linear mapping -- recoupling framework for trend components and complex-domain linear projections for seasonal components. Extensive experiments validate that CATS-Linear with fixed hyperparameters achieves state-of-the-art accuracy comparable to hyperparameter-tuned baselines while delivering SOTA accuracy against fixed-hyperparameter counterparts.